: How can I indicate that a particular relationship between two male characters is purely brotherly (Philia) rather than romantic (Eros)? One of the four forms of love Greek philosophy recognised,

Have them emotionally connected in a way, that if one of them died, they would feel a part of themselves die too. They can act a little like they are in love, but still make it obvious that they are not.

Seeing as they are two guys, you are going to have a harder time. Two guys in a close relationship are almost always assumed to be gay, while two girls in a close relationship are almost never considered gay. Even as a gay guy, I find this annoying.

Hope this helps.

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It's interesting that you identified Kirk and Spock as phillia as a lot of fan fiction terms are traced to Star Trek fandom having a Kirk Spok eros relationship as a core theme of Fan fiction. In fact in fan fiction the term "slash" fiction denotes that the work will deal with two characters in a romantic relationship (often homosexual) that isn't supported by canon derives from the format Star Trek fan fics uses to denote that there would be a romantic relationship between Kirk and Spock (Kirk/Spock, pronounced "Kirk Slash Spock" when spoken).

Suffice to say, it's difficult and the two big aversions I have seen have some way of steering close into the issue rather than avoiding it.

My first example is that of Cory, Shawn, and Topanga in "Boy Meets World". Cory has a phillia relationship with Shawn and a Eros relationship with Topanga and it's generally accepted that as close as Cory and Shawn are portrayed, they aren't in a homosexual relationship with each other. Shawn was often portrayed as a womanizer and Cory and Topanga are middle school sweethearts (and Cory didn't like her initially) with Cory seeking Shawn's advise with relationships. As the series progressed, their friendship avoided the homosexual implication by steering into the skid. Later seasons would show Cory and Shawn acting like a romantic couple without either party thinking it was weird and Topanga (who was Cory's wife in some instances) expressing faux-jealousy of Shawn and reminding Cory that she is his girlfriend/fiance/wife. In the few times she was outright jealous, Cory's lesson was normally his closeness with Shawn does come off as weird to people who don't get that they're practically brothers, not buddies, while Topanga's lesson was that she has to accept that Cory and Shawn have an extremely close bond, but Cory is oblivious about the optics and isn't trying to hurt their marriage.

The other example is Frozen, where the fandom is usually more likely to think Elsa is gay, they would much perfer a female love interest to appear in the as of writing unreleased sequel than to pair Elsa with the other female lead, her younger sister Anna. Part of the reason for this is that Frozen's plot is resolved by Anna's discovery that "True Love" can be a phillia relationship rather than an eros relationship. In fact, this twist was set up so that the audience would assume the moral was a lesson about moving too fast in a romantic relationship as the audience was already critical of Anna's first assumption of a kiss from Hans being a "True Love". When played out, the first punch of Hans having no love for Anna, but feigning it well (the audience was prepared for him to just not be the one for Anna, as the film highlighted Anna moving too fast with a guy she just met... they weren't prepared for Han's response) was also perfect to set up the Red Herring Love interest of Christian (red herring being that Anna still believes the lead guy kissing her will break the curse... Christian and Anna's relationship is moving much slower) and both the audience and Anna aren't considering that the use of Love can describe non-romantic relationships. It's also helped that while Anna's curse breaking action is definately an act of love, it is a very aromantic action, and the curse is broken by her performing this action, rather than someone else showing they love her (compared to other Disney characters aflicted with curses that require true love to break, Snow White, Aura (Sleeping Beauty), Ariel (Little Mermaid), and the Beast (Beauty and the Beast) all have the curse lifted by showing someone else is capable of loving them, where as Elsa lifts the curse by showing she is capable of loving someone against despite her own self-interests).

These titles work because in both cases, the narrative addresses the issue of the existence of more forms of love than romantic love, rather than try to excise love from the non-romantics relationships.

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As others have pointed out, you can't stop people from shipping whomever they want, but you can deflect some of the energy. If plausible within the scope of the story, center a romantic relationship between two other male characters in the main narrative as a contrast. You say you already have LGBT characters, so this shouldn't be introducing new challenges into the story. The romance doesn't have to be any more detailed than other romantic relationships in your story, but it should be explicitly indicated for this to work.

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Explore your setting
What is your setting? As a modern Greek, when a man is married, nothing short of kissing the other man on the mouth will make me suspect sex between them. Because normally (all exceptions deeply respected) marriage in a modern setting signals for me: „I have very strong personal, emotional and sexual interest in this person“ and hints (be the addressee male or female) simply cannot break that expectation (if for example I see a married friend spank a woman’s/man‘s ass, I will assume it is a joke. If I see him squeezing that ass ferociously, I will assume he is intent on breaking his marital vow).
Is marriage forced in the setting? Homosexuality concealed etc.? Is homosexuality highly en vogue, so that we would likely know about it, if it were the case?
What marriage rites did they participate in? Many (for instance Christian rites) emphasise fidelity. Are your characters true to their words?
Use dialogue
What tone do your characters use? If they are Rambo-asshole types you can have one say:
„I hate when my wife is away in Connecticut and I can’t give her a pl…ing for three months!“
Or:
„If you keep looking at that woman’s ass like that I’ll tell your wife and you’ll have to ‚hand wash‘ for weeks“.
Or you can have a wife say it:
„Keep staring at that youngster and your spaceship won’t hangar ever again!“
Obviously my English slang is not as good as my Greek slang, but you get the idea.

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I really don't understand why you have to point out anything at all.
As long as there is no clear indication of an erotic relationship, the non-prejudiced reader will not assume that there is one.
As a writer, you shouldn't try to write against the projections of those who see their preconceptions, desires, or fears in everything that they encounter, because that will irritate your other readers who then start to wonder why you negate something they didn't read into your text in the first place.
If, on the other hand, a majority of your beta readers think that you are building towards an erotic relationship, then you probably see your characters in that way and haven't become clear about their relationship yourself. You then need to do some more character development.
I clearly would never take extra precautions against being misunderstood by those who are out to misunderstand everything.

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The same way you can point out the same relationship between any pairing people think/assume are romantically involved, show how funny and/or gross they find the idea that they could ever be more than friends. Someone suggesting that they're together gets a laugh until they realise the person is serious at which point the outrage and disgust set in. This works even better for characters who are related but it works well enough for any pairing that aren't a couple. Supernatural does this very well, repeatedly, with the Winchesters, as does the Emberverse in which it is applied to a number of both same sex and mixed gender pairs at different times.

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Explain why are your characters more devoted to each other then to their wives

Marriage supposed to be closest bond between two human beings. Of course, that is the theory, in practice things often end up differently. Your characters could have various problems in marriage, for example they could have married based on good looks and those looks are gone, they could have devoted to much time to kids and kids have grown up etc ... Since they are very close friends they could discus these problems with each other, and thus establish they are still attracted to female sex.

One usual and somewhat lazy plot device to establish two characters as heterosexual red-blooded males is to set them up to make comments about other women ("Catherine is a hot piece of tail ..."). This of course could be altered to sound more sophisticated ("Catherine is indeed one exquisite woman ..."), depending on circumstances of your story.

Key would be not to overdo it, and not to make your story some politically correct garbage were you would write some long-winded explanation why your characters are not homosexual, but still support their rights as you do as an author. Instead, simply throw few casual sentences that establish them as heterosexuals and move on.

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It's not you, it's readers

How can I indicate that a particular relationship is all Philia, no Eros involved?

You can't. It's not you; it's them.

When someone ships Spock and Kirk or the Winchesters or Batman and Robin, they are not saying anything about how the characters were written. They are saying that they perceive characteristics about the characters that they would like to see the characters together.

The same thing is true of opposite sex shipping. Many times fans will want to pair characters even if there is no reason to put the two together. Part of this is that movies and TV tend to include romantic relationships to broaden the story's impact. People who don't like the main plot may still enjoy the subplot. They may identify with half of the pair and be attracted to the other half. Speculating about such relationships then becomes part of the attraction of watching movies. The relationships may make no sense otherwise (dwarf/elf relations in Tolkien?). But movie logic says that some pairing is going to be shipped.

Slash shipping also has an extra component. It may be that the shipper is saying that both characters are attractive to the shipper. Shipping them allows for erotic fantasies involving both. Without that, the fantasy would have to pick between the cool, logical Spock and the demonstrative and passionate Kirk. Slash shipping offers both in the same fantasy.

Male vs. female slash

But for some reason, a strong bond between female friends is accepted, whereas whenever men are involved, sexual overtones get added in.

I think that you are just wrong on this. A quick Google finds at least one example, Supergirl Recap: Kara and Lena Practically Beg for Slash Fiction About Them in “Luthors”:

I adore Kara and Lena’s friendship. And the chemistry between her and Melissa Benoist as Kara is off the chain. And yes, I know, they’re just becoming close friends … but when they were sitting on the couch together and Lena was thanking her profusely for believing in her … tell me you didn’t think Lena was going to lean in for a kiss. Was it just me? Maybe it was the leather top Lena was wearing, I dunno.

There is no evidence that the show intends Kara and Lena to be lovers. Both have shown interest only in men (including the same man, both have dated Jimmy Olsen). If one were to have a lesbian relationship, Alex (short for Alexandra for those who don't watch the show) seems like a far more appropriate partner. This is especially so for Kara, as her dating any other woman might well be seen as a rejection of Alex. Listen to Alex describing her perfect woman sometime, and then think about how many of those boxes that Kara fits.

This also touches on a big problem that homosexuals (and heterosexuals) have. It's not always obvious whether someone is interested in you in the same way that you are interested in the other person. Alex may be sexually attracted to this beautiful woman with whom she has had close contact for years. Alex may be just now recognizing that she is attracted to women (not universal but not uncommon among homosexuals). It may be hard for her to recognize how she feels about Kara. And if she does recognize it, how would she interpret Kara's actions? If Kara behaves the same way as Alex when Alex recognizes that in her case, it's romantic interest, isn't it reasonable to think that Kara feels the same way?

It's not the Supergirl writers who are shipping these relationships. It's the fans.

The point is that people do slash ship female relationships. Off the top of my head, Xena/Gabrielle comes to mind as well. But so much fiction has male leads that you may just be seeing a natural concentration on those characters. Quite often female slash shipping is seen as intentional while male slash shipping is more obviously not.

Child sexual abuse

People who have been sexually abused as children sexualize non-romantic relationships. They had their own non-romantic relationships with their uncles, aunts, babysitters, etc. sexualized. This colors the rest of their relationships and their perceptions of relationships in fiction.

You didn't abuse them (at least I hope not), but they will still view your work in terms of their lives. This is not stoppable by anything that you do. You have no control how others perceive your work.

General vs. specific

It may be true that there is something that you may be doing in this specific work where you are encouraging readers to view the characters together. That's really impossible to analyze without the work itself. Let people read the work. If they start slash shipments, ask them why. Address their points with appropriate rewriting if you think their interpretation will be common.

In general though, slash shipping is not about the author's writing but about the reader. It is out of the author's control.

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The problem is, you CAN'T prevent people from making slashfics about your characters. Supernatural is the greatest proof of this you could ever have.
Sam and Dean Winchester are brothers. Not even half, step-, or adopted brothers. They are 100% blood brothers, and the show makes sure to remind us of this constantly. Still, Win-cest fics are some of the most popular slashfics for Supernatural fans, alongside Destiel fics. You can't avoid it.
There's a term in Japanese for these types: 腐女子 (pronounced: fujoshi). It refers to girls who avidly read yaoi or "boys love" stories. In the most extreme cases, the ones that made the term a "necessity" of sorts, fujoshis take even the most mundane, ordinary interactions between two males and fantasize about as many possible sexual undertones their words and actions could possibly have, no matter how deluded the fantasy may be. Of course, these types know that with real people (unless the objects of the fantasy are celebrities), they're just fantasizing, but once they start reading or watching fiction, they'll make every justification for why they're right, why they should be right, or why it's just right for their fantasies to be reality. (This actually got to such a point, an anime called "Kiss Him, Not Me" starring a fujoshi main character was released making fun of the personality type, while also humanizing it.) This term also can work to describe western slashfic writers too. (The term "fudanshi" is the male equivalent of this word. For simplicity, I'll generally only use "fujoshi" in this, but "fudanshi" are included in my intent/meaning.)
This isn't to say a little healthy imagination can't be a good thing, but with the (hopefully) fringe members of this already extreme group, so much as walking past each other and not saying a word is confirmation in the fujoshi's mind. I repeat, this is for the extreme and only in regards to fiction (and celebrities). (If you want proof of fujoshis in regards to celebrities, take a look at the Markiplier x Jacksepticeye slashfics.)
When it comes down to it, most slashfic writers tend to be the more avid fans of a work, so it makes sense that they'd be avid fans of other things as well. If two characters of the same sex have any kind of relationship, no matter the type, you won't be able to avoid a fujoshi's mislabeling of the relationship. It's an unwritten sub-law of rule 34 of the internet.

"If it exists, there is porn of it. No exceptions."

"If there's any form of relationship between two characters of the same sex, a fujoshi/fudanshi has written a slashfic of it. No exceptions."

Now the sub-law has been written. It's worth noting
If you want to minimize the risk, your best bet is to minimize the exposure your story gets. Fujoshi and fudanshi are everywhere nowadays. If your story gets read by only a few people, you can probably avoid fujoshis/fudanshis from mislabeling relationships. However, it's safe to assume that the larger your readership gets, the more likely a fujoshi/fudanshi will romanticize/sexualize otherwise innocuous relationships.

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Have them act like male philos friends and not eros lovers.

For example, if they call each other "Fatso" and "Bullet-head", readers will tend to think of them as friends. If they call each other "Darling" and "Honey-buns", readers will think of them as lovers.

Maybe that's obvious, but I can think of many more subtle examples. If they have an argument and then make up and they hug, that will be a possible sign that they're lovers. If they have an argument and then make up and they say, "Hey, sorry Fred" and "I get it. We're good.", that's more like friends. Could two philos friends hug? Of course? Could too lovers say "sorry" and "that's ok"? Sure. But it's the sort of thing that adds up. If I read a book -- or saw two real men -- who did one "maybe lover" thing and ten "probably friend" things, I'd likely conclude they're friends, not lovers. And vice versa.

I've read plenty of books, seen plenty of movies, etc, where two men are friends and it never occurred to me to think they might be gay lovers, because they never act romantic towards each other.

I think that to the average heterosexual, the idea that two men might be in a gay relationship is out of the ordinary enough that they won't tend to think of it unless you hit them over the head with it. Homosexuals are like 3% of the population, after all. Like, if a story is set in the United States, I'll generally assume that all the characters are American citizens unless you tell me otherwise or give me strong clues. Not because I am prejudiced against non-Americans, but because the statistical reality is that most people in the US are US citizens. I assume that all characters are of roughly average height unless told otherwise, even though I am well aware of the existence of dwarfs. Etc.

Homosexual readers appear to be more likely to see or imagine homosexual relationships. To an extent I can see this: it's presumably part of their daily lives. (Still: I'm white. But if I read a story set in Nigeria, I think I'd assume the characters are black unless otherwise specified. I wouldn't assume they are white just because I'm white. Whatever.)

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There are three frames of reference here: The author's intention, the way the audience receives the characters, and, arguably (but controversially) whatever reality the characters take on in themselves.

Of the three, you're really only responsible for (and fully in control of) the first. Write the characters in whatever way makes sense to you, and seems most true to their own reality as you perceive it, and the story you want to tell. Fans who want to see a relationship between ANY two characters can always build a case to support that, no matter what you do. Part of the issue is that many of the aspects of a strong platonic relationship are similar to that of a romantic relationship, and the ones that are not are the same ones that would be repressed or hidden in a clandestine relationship, or in the case of unwanted feelings. The more you, or your characters, try to deny a romantic side to this relationship, the more convinced people are that it exists. Ironically, the best real-life signal that a relationship is genuinely platonic is a lack of tension or conflict around the topic. When two friends aren't worried or bothered at all by being perceived as a couple, it usually means they aren't one. You can even lampshade this a bit by having the friends joke about how everyone thinks they're secretly involved.

A lot also depends on context. A historical novel, or one placed in a setting where relationships are more often homosocial than homosexual will have less of a challenge in justifying the kind of relationship you want to present.

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I don't know if this helps, but I think war movies do this very well. The Deer Hunter, Saving Private Ryan, some movies involving gangs, or cops on a mission. The series Vikings has elements of this brotherly love too. Many police movies and series show the same thing amongst fellow cops without making it sexual; on NCIS we don't think the main character Jethro Gibbs is in romantic love with any of the several men he has had close relationships with, or even lived with. But he is stoic, doesn't like to talk, and all these men have been in the trenches with him, in either war or police work. When they hang out, they do male things, eat steak and watch football (a metaphor for war).

I'm analyzing off the top of my head, so your own interpretation is as valid as mine, but I think the lethal consequences of conflict can plausibly offset any Eros in the relationship and the risks taken together or for each other prove the "love" aspect you are looking for.

Any form of tenderness (holding hands, kissing, banging it out) is just not in the cards in such situations; and the male characters never have any "tender moments" with each other, they aren't gazing into each other's eyes. Typically when relating any emotional back story, men are not looking at each other, and if one gets emotional the other responds more stoically, and briefly without elaboration. "That sucks, dude." That's it.

The love between them is seldom stated, it is proven by heroic action when the other is in trouble. From memory, I believe they most commonly refer to each other as brothers, not friends, to emphasize the greater commitment. It's a handy tool, because it also reduces any expectation of homosexuality and most people are more ready to accept brothers (or a father and son if the age difference is great enough) can have a deeper non-sexual relationship. You can see this in the film Four Brothers, with Mark Wahlberg: four men (two black, two white), all adopted by the same woman, come together for her funeral ... and to kill the man that murdered her. A war movie of sorts, but you never feel like these men were ever lovers. For one they are all too callous (playing against common gay stereotypes) and secondly the story gives us a very good reason for them to love each other, they grew up together in a rough neighborhood and despite their lethal toughness, they all loved the same kind mother.

IN general I'd say you need a good reason for this philial friendship to exist, and to be plausible, it likely needs to involve mutual protection and co-dependence in response to a dangerous environment. Either one in the past which they both survived, or one in the present where they need each other to survive.

Also, "dangerous" could be metaphorical; entailing political or financial or social survival. In the original premise of "Suits", the friendship of Mike and Harvey is philial, but they share a lie that can cost them a fortune and their careers. (The risk taken by Harvey in not exposing Mike's lie proves his philial love for Mike.)

Added in response to comment: It was mentioned my examples were older. We can scale the dynamic to any age, even boys. Male philial friends are at their best, for some reason, when they are doing projects together, be it kids building a fort in the woods from scrap lumber, or adults investigating a crime.

In Stephen King's The Body, the boys set out "on a quest" to find the body of a missing boy (and do). Very little of the story is about the body, it is about the conversation they have on the way, and actually finding the body is relatively straightforward. But King puts them together through this device of giving them a project that binds them together for a time, with a goal to accomplish.

Projects play against friends being together for any romantic reason, and if your characters are in high school or college or young adults, there is no shortage of projects the guys could work on together. It lets them spend time together, getting something accomplished together, having fun and joking around and being together, demonstrating their complementary skills and shared interests, while doing something not remotely romantic or sexual. Of course you still want some conflict in these interactions, but it doesn't always have to be between the characters, it can be problems moving their project forward, or the friends dealing with somebody else on their project (eg if they were helping out a charity) or opposing their project (eg if they were working on a political campaign, or a business idea with competition).

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But for some reason, a strong bond between female friends is accepted,
whereas whenever men are involved, sexual overtones get added in

I hear this a lot. ‘Let men just be friends!’ And I’m all for it. Men should be free to show affection, vulnerability, and closeness in their friendships just the way women are. It is so uncommon (in western society, at least), that some people find it jarring and immediately jump to the idea that the relationship must be romantic/sexual, because men are only supposed to act that way with their romantic/sexual partners.

On the other hand, have you ever heard a queer woman tell a story of the many times her partner was determinedly referred to as her friend in various scenarios, at a dinner date, holding hands walking down the street, shopping for a bed in IKEA? It’s funny isn’t it? If you want readers to believe your two female characters are falling in love, you better beat them over the head with it. But the lines between friendship and romance may be more blurry than we realise.

So let’s try an exercise. Imagine one of your characters is a woman, the other still a man, and no other aspect of the relationship has changed. Do you think readers would be able to discern the platonic nature? Might the reader still expect this friendship to evolve into romance later, because that’s just what happens in stories?

The common perception of shippers is that they’re squealing schoolgirls who just want to see boys kiss. But there is a significant audience of LGBT folk who simply ship because it feels natural and normal for two same sex characters with a strong bond to fall in love, just as it will feel natural and normal to a straight audience for a male-female friendship to tend that way. The difference is, we don't get to see a whole lot of it in media. Shipping is our representation. Sometimes it's the representation all we have.

The other difference is in the reaction to that assumption. If someone was to ask a man and woman with a close friendship if they are a couple, they will probably just deny it while laughing it off. When it’s two men with a close friendship, there’s discomfort. There’s offense. There’s this whole ‘Let men just be friends without it being gay!’ thing. Well, what's wrong if it had been gay? It’s so subtly homophobic, but significant nonetheless. You can deconstruct the toxic masculinity of denying men close friendships without throwing queer men under the bus.

So my advice is to look at this similar question and do exactly what you would do if your philia pair was a guy and a girl. Don’t make jokes to brush it off. Don't worry about shippers. People are still going to ship them no matter what, and that’s valid. There’s no need to be put off by it.

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Shippers will always mistake close friendships as homosexual, because of all the natural chemistry that comes with written close friendships. Folks will have 'shipping goggles' on no matter what, and open affection between guys (who in fiction and real life alike are expected to be cold, distant and aloof to anyone that isn't their romantic interest) is often just the fuel shippers need.

In terms of how to deal with the phenomenon that is shipping goggles, I'd recommend lampshading it from time to time; accept that it's going to happen and that you can't mind-control readers prone to that sort of thing.

I have a pair of vitriolic best buds in my story, one being a naturally gentle, intellectual and paternal man who's thrust into a leadership position and the other a confrontational, callous, extremely talented archer who can't teach archery to save his life because his skill's largely innate. They argue all the time, but underneath it all, they both like each other and uncompromisingly act in each other's best interests.

When they have a particularly bad argument at one point in the story, they hug it out after making up. Here is where I lay the acknowledgement of the shippers; the callous, brusque one puts on fake machismo saying 'this is so inverted' (the in-universe term for homosexuality; 'this is pretty gay' is the modern equivalent), and the gentle, paternal one then saying 'you don't have to dismiss friendship as inverted, just accept the hug and move on'.

Essentially I both acknowledge the shipping goggles present and roundly mock the idea of it being canon in one fell swoop, while also having a thematic exploration in-universe (namely, deconstructing the idea that all men have to be unfeeling to their friends).

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